Induction Definition and 999 Threads

I apologize in advance if some of my answers don't quite make sense. I'm generally articulate, but not when it comes to physics I'm barely grasping. I did a lab and part of it was dropping a magnet through a coil, which produced a Voltage vs Time graph using LabPro. For trial 1 we had the N...

Homework Statement A flat coil of wire has an area of 0.010 m2and contains 100 turns. Initially the coil is oriented so that the normal to its surface is parallel to a downward constant magnetic field of 0.2 T. The coil is then rotated clockwise through an angle of 30oin a time of 0.10 s...

I am having trouble proving these. I cannot figure out how to get to the conclusion. Here is my attempt. The stuff in red is just side work and is not part of the proof. I always get stuck on these types of problems, can someone offer some tips on how to approach these kind of problems in...

Homework Statement Prove the statement by mathematical induction: 5n + 9 < 6n for all integers n≥2 Homework Equations .. The Attempt at a Solution Proof: let P(n) be the statement, 5n + 9 < 6n P(2) is true because, 34<36. Suppose that P(n) is true. P(n+1) would be...

Homework Statement An electric generator consists of n = 500 turns of wire formed into a rectangular loop with a length of 5 cm and width of 3 cm placed in a uniform magnetic field of 2.50 T. What is the maximum value of the emf produced when the loop is spun at f = 100 rpm about an axis...

Hi, Some times the starting point in MA confuses me, for example (\sum_{i=1}^ni)^2=\sum_{i=1}^ni^3 have we start with 2 or it is enough to show it when n=1 Thanks in advance.

Hello there, I'm having trouble proving this by induction Homework Statement \frac{1}{1(2)} + 1\frac{1}{2(3)}+...+\frac{1}{n(n+1)} = \frac{n}{n+1} Homework Equations For the base case n=1 \frac{1}{1(2)}=\frac{1}{1+1} = \frac{1}{2} = \frac{1}{2} \frac{k}{k+1} +...

I was wondering if induction can apply to different chemical solutions. Take HCl for example. If a negatively charged rod were placed against the beaker in which HCl was held, would the H+ ions be pulled towards the rod. Would the same outcome appear in a neutral solution of NaCl (drawing the...

When a magnet is pushed into a solenoid an induced emf occurs. So if it is a closed circuit then an induced current will flow. But if it is an open circuit then an emf will still be induced but no current this time. So will any poles be formed to repel it? What do they mean by the current...

What will happen when I push a magnets into a solenoid with constant speed throughout? I understand that when the magnet leaves and enters an induced emf will occur, but in the middle no emf will occur. Why is this so? I thought that the magnetic flux linkage changes as it moves in the solenoid?

In this link (https://www.physicsforums.com/showthread.php?t=523874 ) there's an example of proof by induction. Somewhere in the explanation there's the phrase: Why they decided to multiply both sides by x+1?

I am confused by what the book is saying, can someone explain how they got the thing I circled in red?

A question I'm working on and my math book doesn't clarify the answer well enough for me to follow. I'm having some issues at getting the math symbols to work correctly so bare with me!Prove by mathematical induction that if A1, A2, ..., An and B are any n + 1 sets, then: Base step = n = 1 so...

i can't grasp the idea that how is electrostatic induction possible in a conductor. for example, if a negatively charged strip is brought near a metal conductor, the electrons will be repelled to the further end of the conductor thus making the end near the charged rod positively charged...

Homework Statement If (an) — > 0 and \bn - b\ < an, then show that (bn) — > b Homework Equations The Attempt at a Solution

Good Day All, I would like to know if anyone can help with the following; I am running it a few problems and I am not able to find the formulas that will allow me to prove my idea. I have a loop of 20 Gauge magnet wire; it's 24 inches by 2 inches. I'm using this as a detector, but i want to...

Consider the set S defined recursively as follows: • 3 ∈ S, • if x,y ∈ S,then x−y∈S, • if x∈S, then 2x ∈ S, • S contains no other element. Use Structural Induction to write a detailed, carefully structured proof that ∀ x ∈ S, ∃ n ∈ Z, x = 3n. What I've got is since 3 is in the set...

I have a mountain cabin where 2 water pipes, hot an cold, goes between the bathroom and kitchen. However, they tend to freeze in the winter. The obvious solution is to put a heating wire along the pipes, but access is cumbersome. So I have thought about following solution: I ensure electrical...

Consider the set T defined recursively as follows: • 2∈T, • if x∈T and x>1,then x/2 ∈T, • if x∈T and x>1,then x^2 ∈T, • T contains no other element. Use Structural Induction to write a detailed, carefully structured proof that ∀ x ∈ T, ∃ n ∈ N, x = 2n. I'm not sure how to...

How much power is needed to be able to melt aluminum using induction heating? So I have coil of copper wire around an aluminum cylinder. The aluminum is NOT touching the copper wire. the copper wire have a thickness of 0.5 cm. d = 0.5cm the copper wire is looped 20 times around. N = 20...

What is the heating efficiency of a domestic induction heater as compared to a simple electrical heater and microwave oven? Please give comparison on the basis of Kilowatt hour consumed.

Hi guys, Long time lurker of this forum, but first time poster. Discrete Math is going to be the end of me; I'm just not understanding how to solve problems and write the proofs. Any help would be greatly appreciated. Thanks in advance. The Problem: Let nεZ≥1. Show that...

Homework Statement Define an = (an-1 + an-2)/2 for each positive integer ≥ 2. Use induction to show that: an+1 - an = (-1/2)n(a1 -a0) Homework Equations First show it is true for base case. Assume if it is true for (k), then show it is true for (k + 1). The Attempt at a Solution...

Solved: Is this an induction problem? (1+2+3+ \cdots + n)^2 = 1^3 + 2^3 + 3^3 + \cdots + n^3 , n \ge 1 Provide a derivation of the identity above. I do not know how to begin this problem. I tried to use induction but did not succeed. Also, I honestly do not know what it means by...

When you have a magnet moving up and down a coil. The magnet cuts the field lines. Which generates an AC current in the coil. In my exam, there was a sinusoidal curve showing the generation of AC current. When the curve crossed the x-axis, that point was labelled X. Now at that point was the...

I have an idea of what to do and I have reached the stage but when i am at final stage- I am struggling to simplify as i simply don't understand (1/2)+(2/2^2) +(3/2^3)+...+ (n/2^n) = 2 - (n+2/2^n) so I have done p(k) and p(k+1) this gives me p(k) (1/2)+(2/2^2) +(3/2^3)+...+ (k/2^k)...

By spinning a magnetic field in the presence of conducting wire, how much voltage/current is produced? Thanks.

Homework Statement \int_0^1{x^n (1-x)^r}\,dx = \frac{n!}{(r+1)(r+2)...(r+n+1)} Homework Equations n≥0, r≥0 The Attempt at a Solution i solved it for the case n=0, where RHS and LHS are the same. however, I am having trouble integrating the LHS for the induction step where n=k+1. i'm trying...

prove by induction that, 1) a^(m+n) = a^m + a^n 2) (a^m)^n=a^(mn) 2. Homework Equations -- mathematical induction 3. The Attempt at a Solution the equations hold for a = 1. let's say the equation hold for a = s; then s^(m+n) = s^m + s^n now for a = s+1; (s+1)^(m+n) = (binomial expansion of...

In preparation for an upcoming physics exam I have been going through some past paper questions. This question is from the multiple choice section of the paper, so while I can check the answer there is no source from which I can see it being worked through. Homework Statement An aircraft...

Homework Statement I am taking the readings of voltage/current in a small induction generator; the readings are conveyed as negative on the voltage/current sensors on my data-logger, and positive on the multimeter in both areas. When the magnet passes through the coil, and power is generated...

Hi, I was designing a High Power High frequency Induction Heater inverter. I've choose H-bridge configuration for the inverter and IR2110 gate drivers to drive the bridge. As the IR2110 is a half-bridge driver i'll use two of them to drive the both sides. I've done a rough circuit(just...

What will happen if the rotor speed becomes larger than the synchronous speed for induction motor?

Homework Statement Show that it is possible to arrange the numbers 1, 2, ... n in a row so that the average of any two of these numbers never appears between them. [Hint: Show that it suffices to prove this fact when n is a power of 2. Then use mathematical induction to prove the result when n...

I understand that electromagnetic induction is determined because of a moving electric charge in a magnetic field, but why is the motion necessary? Why is it that motion causes electromagnetic induction and it isn't possible without motion?

Homework Statement Suppose a and b are real numbers with 0 < b < a. Show that, if n is a positive integer, then a^n - b^n \leq na^{n-1}(a-b) Homework Equations The Attempt at a Solution I'm trying to show this by induction. Let P(n) be the proposition that a^n - b^n \leq na^{n-1}(a-b)...

I'm willing to say that I have a fair understanding of Electromagnetism, at least from a classical perspective, but I was never entirely clear about the difference between, say, the time-varying magnetic field created by an inductor and the Electromagnetic field of light in general. Based on...

Homework Statement 2n-1 Sigma (3i+1) = n(6n-1) i=0 prove for all positive n Homework Equations The Attempt at a Solution It holds true for n=1 5=5 then P: m+1 2m+1 Sigma(3i+1) = (m+1)(6(m+1)-1) or 6m^2 + 11m + 5 i=0 then 2m+1 Sigma(3i+1) = m(6m-1) +...

Homework Statement Let Tn(x)=cos(narccosx) where x is real and belongs to [-1,1] and n E Z+ Find T1(x). Show that T2(x)=2x^2 - 1. Show that Tn+1 (x) + Tn-1 (x) = 2xTn(x) Hence, prove by induction that Tn(x) is a polynomial of degree n. The Attempt at a Solution Since cosθ=x and arccosx=θ we...

1. I don't understand how to prove this. for all n≥1, 10n - 1 is divisible by 9. 3. I've done the basis step. Now I'm on the inductive step. I'm using (10k+1-1)/9=1. I don't know where to go from there. Using algebra just gets me down to 10k+1= 10. And I really don't think that's...

Prove by induction that n^2 + n ≤ 2^n for all integers n≥5 How i did: Case(1) Suppose that n = 5 LHS = 5^2 +5 = 30 RHS = 2^5 = 32 30 ≤ 32 Ok LHS ≤ RHS Case (2) Suppose that's true for n=p≥5. Show that its true for n = p+1 What should i do next ? I had a memory loss here :(

Suppose you are building a sequence consisting of 0 and 1 in such a way that: - you start with 1 - no consecutive 0s are allowed Examples of such sequences are: 1, 1010, 110111101 etc. Empty sequence is also allowed. I want to prove by induction that the number of 0s in such a sequence is...

Homework Statement ( Given: U0=2 and : (U)n+1=(Un^2+Un)/(1+Un) Homework Equations prove that for every n in N : Un>1 The Attempt at a Solution ok for n=0 i got Un+1=2 and 2>1 therefore for n=0 its true. now we assume its true for U=0 and we want to show that Un+1>Un...

Homework Statement The Attempt at a Solution I'm not really sure where to start with this one. I know that in steady state the capacitor will become an open circuit and the inductor a short circuit. I first changed the current source to a thevenin equivalent of 1.2mV. I don't...

Homework Statement Prove by induction that gamma(v+1)(v+1)(v+2)...(v+k)=gamma(v+k+1) for k=1,2,3... Homework Equations Really just using the relation x*gamma(x)=gamma(x+1) The Attempt at a Solution for a basis gamma(v+1)(v+1)=gamma(v+1+1) so holds for k = 1 inductive...

Hi there. I have a current I running throught a tesla spiral coil, and I have to compute the magnetic field at the center of it. The tesla coil has N turns, and an inner radius a, and outer radius b. This is the tesla spiral coil: The courrent enters through the outer cable, and goes out...

Hello! Not sure if this should go here, but it's from a physics textbook. I was reading about charge by induction and the use of an Earth to achieve this. Here's a wonderfully detailed and exquisite image that took many laborious hours to construct. The red and black Earth's are not intended...

Hello everybody, I am doing my reading lately to prepare for some exams to join a mathematics department. And I would very much like, if anyone could help, the solution (or a hint) to the following induction proof. " Show that n^3 + (n+1)^3 + (n+2)^3 is a multiple of 9 " :smile: I...

Homework Statement http://dc10.arabsh.com/i/03594/qn9gr42q192z.png What is the direction of current in ring 2 if : a) ring 2 moves towards ring 1 b) ring 2 moves away ring 1 The Attempt at a Solution I used Fleming right hand rule but I'm not sure if it is true, a) the...

I remember my discrete math course in university, where professor told that we can apply induction only to discrete sets. Yet, neither Wikipedia nor Google say nothing about countability importance for induction. They say that underlying set must be well-ordered. The well-ordering topic says...